"Our final round was really good," Nicklaus wrote on Facebook,"but theirs was even better."

Stenson matched a major championship record by shooting a 63, becoming only the second player to do so in the final round and win.

Mickelson, a five-time major champion who won the 2013 Open, stayed mostly shot for shot with Stenson until the end, his bogey-free 65 not enough.

"I was fortunate to watch every second of today's final round of the Open Championship, and I thought it was fantastic," Nicklaus wrote. "Phil Mickelson played one of the best rounds I have ever seen played in The Open and Henrik Stenson just played better -- he played one of the greatest rounds I have ever seen."

Stenson, 40, became the first male Swedish golfer to win a major championship and moved to No. 5 in the Official World Golf Ranking.

Mickelson, 46, was bidding to become the fourth-oldest major winner and join Nick Faldo and Lee Trevino with six majors. His score of 267 was 11 strokes better than third-place J.B. Holmesandwould have won 140 of the 145 Opens played.

"Phil certainly has nothing to be ashamed of because he played wonderfully," Nicklaus wrote. "Henrik played well from the beginning to end. He drove the ball well; his iron game was great; his short game was wonderful; and his putting was great. Henrik was simply terrific.

"To win your first major championship is something special in and of itself, but to do in the fashion Henrik did it in, makes for something very special and incredible memorable. I'm proud of and happy for Henrik."

Nicklaus, 76, won The Open three times as part of his 18 major championships. But one of the more memorable tournaments was his 1977 loss to Watson at Turnberry, about 20 miles south of Royal Troon.

Watson and Nicklaus had the same score through 54 holes, shooting the same score each round -- including third-round 65s.

Grouped again for the final round, Watson shot 65 to Nicklaus' 66 in what is considered one of the sport's epic showdowns. Nicklaus finished 10 strokes ahead of Hubert Green, who famously quipped afterward: "I won the golf tournament. I don't know what game those other guys were playing."

Said Nicklaus on Sunday: "Some in the media have already tried to compare today's final round to 1977 at Turnberry, with Tom Watson and me in what they called the 'Duel in the Sun.' I thought we played great and had a wonderful match.

"On that day, Tom got me, 65-66. Our final round was really good, but theirs was even better. What a great match today."